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On dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\)

Abstract

We discuss dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\). In particular, we classify all such dual hyperovals if the ambient space has dimension 7 or 8. We also determine the bilinear dual hyperovals in the case of an ambient space of dimension 9 or 10. A classification of all dual hyperovals in dimension 9 seems possible in the near future.

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Correspondence to Anton Betten.

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Betten, A., Dempwolff, U. & Wassermann, A. On dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\) . J. Geom. 108, 75–98 (2017). https://doi.org/10.1007/s00022-016-0326-2

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  • DOI: https://doi.org/10.1007/s00022-016-0326-2

Mathematics Subject Classification

  • 51E21

Keywords

  • Dual hyperoval
  • enumeration
  • finite projective geometry